agglomeration elasticities in new zealand · new zealand david c. maré motu economic and public...

Agglomeration elasticities in New Zealand

David C. Maré Motu Economic and Public Policy Research Trust Daniel J. Graham Centre for Transport Studies, Imperial College, London NZ Transport Agency Research Report 376

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© 2009, New Zealand Transport Agency

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Maré, D. C.,1 and Graham, D. J.2 2009. Agglomeration elasticities in

New Zealand. NZ Transport Agency Research Report 376. 46 pp.

1 www.motu.org.nz [email protected]

2 Centre for Transport Studies, Imperial College, London SW7 2BU

[email protected]

Keywords: agglomeration, productivity

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Acknowledgments

The work in this paper has been funded by the New Zealand Transport Agency, and through

Motu’s Infrastructure programme funded by the Foundation for Research Science and Technology

(FRST grant MOTU0601). Special thanks to Ernie Albuquerque for his perceptive and challenging

input and comments, and to Arthur Grimes, Richard Fabling and Vicki Cadman for helpful

comments on earlier drafts.

Disclaimers

The opinions, findings, recommendations and conclusions expressed in this report are those of

the author. Statistics NZ or the Ministry of Economic Development take no responsibility for any

omissions or errors in the information contained here. Access to the data used in this study was

provided by Statistics NZ in accordance with security and confidentiality provisions of the

Statistics Act 1975. Only people authorised by the Statistics Act 1975 are allowed to see data

about a particular, business or organisation. The results in this paper have been confidentialised

to protect individual businesses from identification. The results are based in part on tax data

supplied by Inland Revenue to Statistics NZ under the Tax Administration Act 1994. This tax data

must be used only for statistical purposes, and no individual information is published or disclosed

in any other form, or provided back to Inland Revenue for administrative or regulatory purposes.

Any person who had access to the unit-record data has certified that they have been shown, have

read and have understood section 81 of the Tax Administration Act 1994, which relates to privacy

and confidentiality. Any discussion of data limitations or weaknesses is not related to the data's

ability to support Inland Revenue's core operational requirements. Any table or other material in

this report may be reproduced and published without further licence, provided that it does not

purport to be published under government authority and that acknowledgement is made of this

source.

Abbreviations and acronyms

AES Annual Enterprises Survey

GST Good s and services tax

LBD Longitudinal Business Database

LBF Longitudinal Business Frame

LEED Linked Employer-Employee Dataset

NZTA New Zealand Transport Agency

PBN Permanent business number

RME Rolling mean employment

5

Contents

Executive summary .............................................................................................................. 7

Abstract ................................................................................................................................ 8

1 Introduction ................................................................................................................ 9

2 Background............................................................................................................... 10

3 Methods .................................................................................................................... 12

3.1 Estimation........................................................................................................ 14

4 Data: the prototype Longitudinal Business Database ............................................. 17

4.1 Production function variables........................................................................... 18

4.2 Effective density ............................................................................................... 18

5 Results ...................................................................................................................... 22

5.1 Aggregate estimates ........................................................................................ 22

5.2 Estimates by one-digit industry ........................................................................ 25

5.3 Estimates by region.......................................................................................... 29

5.4 Factor augmenting effects and price effects ..................................................... 34

6 Summary and discussion ......................................................................................... 40

7 Future directions ...................................................................................................... 41

8 References ................................................................................................................ 42

Appendix A: Comparability between different data sources: AES and IR10 ................ 44

Appendix tables.................................................................................................................. 45

7

Executive summary

Agglomeration economies describe the productive advantages that arise from the spatial

concentration of economic activity. When firms locate in close proximity to each other a

number of tangible benefits are thought to emerge, for instance, in the form of increased

opportunities for labour market pooling, in the sharing of ‘knowledge’ or technology, in

process specialisation within the industry, or in the efficiency of input-output sharing.

While a vast literature exists overseas there are only a small number of empirical studies in

New Zealand that estimate the strength of agglomeration effects of productivity. This paper

extends previous analyses by explicitly estimating a production function that accommodates

firm-level variation in productive inputs. It is thus able to estimate the impact of

agglomeration on multi-factor productivity. The panel structure of the data in the current

paper also permits controls for firm-level heterogeneity.

This main focus of this report is to estimate agglomeration elasticities for New Zealand for

use in the economic evaluation of transport investments. The New Zealand Transport Agency

(NZTA) publishes an Economic evaluation manual that includes guidance on how to quantify

agglomeration impacts as a benefit of transport investment. The NZTA’s manual includes

estimates of relationship between density and productivity based on estimates from the

United Kingdom, adjusted to reflect the lower levels of density in New Zealand. This study

provides the first set of empirical estimates of agglomeration elasticities based on

New Zealand microdata.

The agglomeration elasticities are estimated using longitudinal microdata on enterprises

based on a translog function. In deriving agglomeration elasticity estimates a range of

conceptual and empirical issues are addressed related to the calculation and interpretation of

the elasticities. This study examines the influence of non-random sorting of heterogeneous

firms across locations and considers variations in agglomeration elasticities across industries

and locations. It also discusses the strengths and weaknesses of alternative controls for firm

heterogeneity and sorting.

In terms of results, agglomeration elasticity estimates are provided on an aggregate, one-

digit industry and regional basis.

In terms of aggregate results not controlling for enterprise heterogeneity and sorting, the

agglomeration elasticity is 0.171. This implies that firms in locations with 10% higher

effective density have 1.7% higher productivity. Controlling for productivity and density

differences across regions and industries reveals that around 70% of the cross-sectional

relationship between effective density and productivity is attributable to observable

differences in regional industry composition. The estimated elasticity is reduced to 0.048.

When enterprise composition differences are fully controlled by including fixed effects the

estimated elasticity is reduced by more than 90% from 0.17 to 0.0015.

When we relax the constraint that production function parameters are common across all

industries the pooled estimates show an agglomeration elasticity of 0.037. Controlling for

the local industry composition of enterprises leads to a higher elasticity of 0.069, implying

that, within industries, more productive firms are disproportionately located in lower density

areas. It would appear that the pooled estimates overestimate the productivity impact of

agglomeration, suggesting concerns that composition bias resulting from sorting of

enterprises between locations inflates agglomeration elasticity estimates are unfounded.

AGGLOMERATION ELASTICITIES IN NEW ZEALAND

8

The small difference between the pooled and ‘within local industry’ estimates using industry-

specific production functions suggests that the bias arising from endogenous density may be

relatively small. In contrast, imposing a common production function across all industries

yields a stark difference between pooled and within local industry estimates, pointing to the

invalidity of the assumption of common technologies. Agglomeration elasticities based on

aggregate production functions should, at a minimum, control for heterogeneity across local

industries to allow for this mis-specification. The ‘within enterprise’ specification yields a low

estimated elasticity of 0.010. It is not possible to distinguish whether this reduction is a

consequence of the sorting of more productive enterprises into denser areas within regions,

or of the attenuation bias associated with the use of enterprise fixed effects. The aggregate

estimates are shown in table 5.1.

Separate agglomeration elasticities are estimated by one-digit industry and are shown in

table 5.2. The reported coefficients are for a linear density specification. Agglomeration

estimates for pooled ‘within local industries’ and ‘within enterprises’ were calculated. The

pooled estimates were generally similar to the NZTA estimates based on United Kingdom

estimates adjusted to allow for significant differences for densities. Controlling for sorting of

enterprises across local industries leads to generally higher estimated agglomeration

elasticities, with the only exceptions being the relatively small education and cultural and

recreational service industries. The impact of controlling for enterprise fixed effects is to give

lower estimates, with the exception of agriculture, forestry and fishing. Agglomeration

elasticity estimates become insignificant in six industries, including finance and insurance.

The reduction in estimated elasticities probably reflects the consequent imprecision of the

enterprise fixed effects estimates rather than sorting alone.

On balance, the ‘within local industry’ estimates in column (3) of table 5.2 provide the best

indication of industry-specific agglomeration elasticities. While they are probably biased by

the sorting of high productivity firms into areas it is not clear how large the bias is, or even

the direction of the bias.

Agglomeration elasticities also vary across regions, from a low of 0.48 in Canterbury to a

high of 0.177 in Northland. High-density regions of Canterbury, Wellington (0.063) and

Auckland (0.056) have lower agglomeration elasticities than less dense regions, consistent

with decreasing returns to agglomeration. Table 5.3 shows the agglomeration elasticities

across regions.

Abstract

This paper analyses the relationship between the multi-factor productivity of New Zealand

businesses and the effective employment density of the areas where they operate.

Quantifying these agglomeration elasticities is of central importance in the evaluation of the

wider economic benefits of transport investments. We estimate that firms in an area with 10%

higher effective density will have productivity that is 0.69% higher, once we control for

industry-specific production functions and the sorting of more productive firms across

industries and locations. We present separate estimates of agglomeration elasticities for

specific industries and regions, and examine the interaction of agglomeration with capital,

labour and other inputs.

1 Introduction

9

1 Introduction

Firms in locations with dense economic activity are more productive than firms in less dense

areas. An extensive economics literature exists that quantifies the strength of this

relationship, and evaluates alternative explanations. Recent reviews of this literature include

Duranton and Puga (2004) and Rosenthal and Strange (2004).

The current paper adds to this literature in several ways. First, it presents the most complete

empirical analysis of agglomeration effects for New Zealand, adding to a small existing

literature. Second, it presents a microeconometric analysis of the impact of agglomeration on

the multi-factor productivity of New Zealand firms. This has been achieved by using a new

longitudinal unit record dataset of firms covering a large proportion of the New Zealand

economy. The dataset enables us to examine the strength of agglomeration effects for a

comprehensive range of industries, and to test alternative ways of controlling for firm

heterogeneity that may bias agglomeration elasticity estimates.

The analysis and findings are of general interest in advancing our understanding of the

nature and extent of productivity advantages of urban activity. In addition, the estimates of

the elasticity of multi-factor productivity with respect to employment density have specific

relevance to the evaluation of transport funding proposals. The New Zealand Transport

Agency (NZTA) publishes an Economic evaluation manual which includes specific guidance on

how to quantify agglomeration impacts as a benefit of transport investment. Following

Graham (2005b), the productivity benefits of transport improvements are included as a ‘wider

economic benefit’ of transport improvements. Transport investments serve to facilitate a

higher density of economic activity. To the extent that this higher density is associated with

productivity improvements, the returns to investments will be greater. The NZTA’s manual

includes estimates of the relationship between density and productivity for each of nine

different industry groups (NZTA 2008, p A10–3). These figures are based on estimates from

the United Kingdom, adjusted to reflect the lower levels of density in New Zealand (Graham

2007).

The main focus of this report is on the direct estimation of agglomeration elasticities for

New Zealand, for use in the economic evaluation of transport investments. It provides the

first set of empirical estimates of agglomeration elasticities based on New Zealand microdata.

It confirms the general cross-sectional aggregate and industry patterns found in international

studies and extends the literature by exploiting the panel structure of the prototype

Longitudinal Business Database data to control for the biases arising from higher productivity

firms sorting into denser locations. In deriving these estimates, it highlights a range of

conceptual and empirical issues related to the calculation and interpretation of agglomeration

elasticities. It examines the influence of non-random sorting of heterogeneous firms across

locations and considers variation in agglomeration elasticities across industries and locations.

It also discusses the strengths and weaknesses of alternative controls for firm heterogeneity

and sorting.


10

2 Background

Agglomeration economies are positive externalities derived from the spatial concentration of

economic activity. When firms locate in close proximity to each other a number of tangible

benefits are thought to emerge, for instance, in the form of increased opportunities for

labour market pooling, in the sharing of ‘knowledge’ or technology, in process specialisation

within the industry, or in the efficiency of input-output sharing. Thus, spatial concentration

gives rise to increasing returns which theory tells us will be manifest in higher productivity

and lower average costs for firms. .

Since transport investments can increase the scale and efficiency of spatial economic

interactions by lowering travel times and improving connectivity, we might expect positive

external effects via agglomeration economies. This is the essence of the case for including

‘agglomeration benefits’ within transport appraisal. Agglomeration economies are driven by

access to economic mass, or in other words, by the access that firms have to other firms in

similar or dissimilar industries, to labour markets, and to markets more generally. Transport

provision is an extremely important determinant of accessibility and thus exerts a crucial

influence on the level of agglomeration experienced by firms. Where there are constraints in

the transport system, or where the system works inefficiently, we would expect negative

consequences for the generation of agglomeration economies. When we make new

investments in transport we change the economic mass that is accessible to firms with

positive consequences for the agglomeration economies these firms enjoy.

A key point that should be emphasised in relation to the potential agglomeration benefits of

transport investment is that these arise as a result of externalities or market imperfections.

This is important because conventional methods of transport appraisal, based on

quantification of the value of travel time savings, generally assume perfect markets and

constant returns to scale. Thus, any agglomeration effects should, in theory, be additional to

the benefits of transport investment captured under a standard approach.

An excellent theoretical account of the link between transport and agglomeration is set out

by Venables (2007). He shows that we can quantify the agglomeration benefits of transport

investments if we know:

• the change in access to economic mass that will result from making some transport

intervention

• the amount by which productivity will rise in response to an increase in agglomeration.

This latter quantity, the elasticity of productivity with respect to agglomeration, is the subject

of this report.

The economics literature has identified a range of possible sources for higher productivity in

more dense areas. A common grouping reflects the work of Marshall (1920), who discussed

the advantages of thick labour markets, ease of linkages to input and output markets, and

knowledge spillovers arising from proximity to others in the same industry (localisation).

Each of these potential sources is consistent with agglomeration effects - the observed

positive relationship between agglomeration and productivity. Observing such a positive

relationship is thus uninformative about the underlying nature of agglomeration effects. The

problem of identification extends also to microeconomic theory. Duranton and Puga (2004)

summarise agglomeration theories under the headings of sharing, matching and knowledge

spillovers, and note that more than one mechanism may be consistent with each of the

1 Introduction

11

sources that Marshall identified. It is perhaps unsurprising, then, that the empirical literature

on agglomeration effects, summarised by Rosenthal and Strange (2004), continues to

struggle in identifying the sources of agglomeration effects.

Many studies have, however, quantified the strength of the relationship between economic

performance and density of activity. An influential study by Ciccone and Hall (1996) estimates

an elasticity of total factor productivity to employment density of 0.04 across the United

States. Graham (2005b) surveys empirical estimates of agglomeration elasticities and finds

that the majority of estimates are between 0.01 and 0.10. In a more extensive meta-analysis,

Melo et al (2009) find a median estimate of 0.041.

One challenge facing many of the reviewed studies is to identify a causal effect of density on

productivity. It is clear that denser areas are more productive but this may reflect other

factors that are positively associated with both density and productivity. It is more difficult to

establish that an increase in density would necessarily lead to an increase in productivity. The

challenge is even greater for studies that analyse the relationship between public

infrastructure, such as transport infrastructure, and productivity (Eberts and McMillen 1999).

In this case, there is the confounding issue that infrastructure investments may be

deliberately directed towards high-productivity areas, meaning that simple correlations

between investments and performance may further overestimate the productivity impacts of

infrastructure. Transport investments will also have wider general equilibrium impacts.

Ignoring these may, however, lead to either an overestimate or an underestimate of the true

impact. As emphasised by Haughwout (1999), increases in density as a result of transport

investments may be offset by reduced density in other areas. In contrast, equilibrium effects

may reinforce the ‘first-round’ benefits. Venables (2007) uses a computable general

equilibrium model to demonstrate the compounding benefits of transport investment

externalities, which are further reinforced by interactions with the tax system.

There is a small number of empirical studies in New Zealand that estimate the strength of

agglomeration effects on productivity. Williamson et al (2008b) report an elasticity of around

0.03 between employment density and average earnings in Auckland using data from the

2001 Census. Williamson et al (2008a) extend this analysis by adjusting for differences in

industry and qualification composition of different areas, with a resulting elasticity estimate

of 0.099.1 Maré (2008) examines the relationship between employment density and labour

productivity, and estimates a cross-sectional elasticity of 0.09 between area units within

Auckland region. Controlling for area fixed effects reduces the estimated elasticity to 0.05

and the relationship becomes insignificant when the relationship is estimated in first

difference form. These estimates control for three-digit industry composition, but not for

capital intensity of firms.

The current paper extends previous analyses by explicitly estimating a production function

that accommodates firm-level variation in productive inputs. It is thus able to estimate the

impact of agglomeration on multi-factor productivity. The panel structure of the data in the

current paper also permits controls for firm-level heterogeneity.

1 Note that the two estimates are not directly comparable because of differences in specification and

evaluation. Williamson et al (2008b) reports estimates from an equation of Income = a+b*log10

(Density).

Williamson et al (2008a) estimates ln(Income) = a+b*ln(Density)


12

3 Methods

Agglomeration effects are characterised as the productive impact of employment in

surrounding areas on a firm’s production technology. It is natural, therefore, to treat local

employment density as an input into a firm’s production function, as represented by the

following equation:

{ } { }( )it i dit itY f E X,= (Equation 1)

where Yit is a measure of firm is gross output in period t; {Xit} is a vector of inputs into

production, and Edit is a vector of employment in surrounding areas, measured at an array of

distances d from firm i. In this paper, we measure employment as total employment locally,

thus focusing on general agglomeration effects. It is possible that firms benefit particularly

from proximity to own-industry employment, the benefits of which will be underestimated by

looking only at the relationship between productivity and total employment locally.

The strength of employment agglomeration can be summarised in a single index, most

commonly by some measure of employment density in a local area. A more general measure

is presented in Graham (2005b), who imposes a constant distance decay factor (α=1) to derive

a measure of effective density (Ui):

( ) ( )

i jji

ij iji

EEU

dAα α

π

≠ ⎛ ⎞⎜ ⎟

= + ⎜ ⎟⎜ ⎟⎝ ⎠

∑ (Equation 2)

where Ei is a measure of employment in area i and dij is the distance between area i and area

j. Ai is the land area of area i, so that iA π is an estimate of the average distance between

jobs within area i.

Distance decay reflects the smaller influence that more distant employment has, compared

with the influence of proximate employment. Distance may be measured as Euclidean

(straight-line) distance, by road distance, or by travel time. Travel time adjustments reflect

the generalised cost of distance, and the impact of congestion in reducing the influence of

distant employment density. Graham (2006b) compares agglomeration elasticity estimates

derived with different distance metrics and concludes that, while the estimated elasticities are

similar, the use of generalised cost rather than distance yields slightly higher estimates

overall and significantly higher estimates in dense urban areas. The processes of sharing,

matching and knowledge spillovers that underlie agglomeration effects probably depend

more on generalised rather than straight-line distance. For the purposes of transport

appraisal, it is however more appropriate to use straight-line distance in deriving measures of

wider economic benefits, as time costs and savings are generally already incorporated in

standard transport models (Graham 2005b, p 118).2

The imposition of a constant distance decay factor of α=1 for all industries may lead to

biased agglomeration elasticity estimates. For instance agglomeration effects that operate

only over very short distance will be harder to identify if Ui includes more distant employment

that is irrelevant to the performance of firms in area i. Direct estimation of variable decay

parameters is beyond the scope of the current paper but would be a valuable robustness and

2 We cannot examine the robustness of our findings to the use of generalised costs, since New Zealand

does not have a national transport model that could provide the necessary measures.

3 Methods

13

sensitivity check in future analyses. Graham et al 2009 have estimated distance decay factors

(α) for four broad sectors of the United Kingdom economy: manufacturing, construction,

consumer services and business services. They use a control function approach to address

potential sources of endogeneity and to allow for unobserved firm level heterogeneity. A non-

linear least squares regression is used to provide a direct estimate of distance decay. The

results show an overall agglomeration effect of 0.04 across all sectors of the economy. For

manufacturing and consumer services they estimate an elasticity of 0.02, for construction

0.03, and for business services 0.08. The distance decay parameter is approximately 1.0 for

manufacturing, but around 1.8 for consumer and business service sectors and 1.6 for

construction. This implies that the effects of agglomeration diminish more rapidly with

distance from source for service industries than for manufacturing. But the relative impact of

agglomeration on productivity is still found to be greater for services than it is for

manufacturing.

Another important result is that the value of α does not greatly affect the magnitude of

estimated agglomeration elasticities. Setting α equal to one produces elasticity results of

much the same order of magnitude. However, the value of α does tend to have an important

effect on the assessment of agglomeration benefits from transport investments. Where α is

high (α > 1.0) agglomeration benefits will also tend to be proportionally higher. The intuition

here is that when distance counts more (α > 1.0) increases in effective density will tend to

give proportionally higher shifts in productivity, although the impact is confined to a smaller

geographic area.

Using the summary measure Ui as defined above, Graham and Kim (2007) incorporate

effective density as a factor-augmenting input to production in a value-added production

function, approximated by a translog form (Christensen et al 1973):

( )

J J Jj h j

i u hjj h j

Jj

ju uuj

Y X U X X

X U U

01 1 1

2

1

1log log log log log

2

1log log log

2

α α γ γ

γ γ

= = =

=

= + + +

+ +

∑ ∑∑

∑ (Equation 3)

where the i subscript has been suppressed and Xj (j=j . . .J) denotes one of J factors of

production. The parameters α and γ are production function parameters, which are potentially

industry-specific,

A common simplification of this specification is to assume that the productive impact of

density is Hicks-neutral rather than factor-augmenting, so that

{ } { }( ) ( ) { }( )j ji dit iit itf D X g U h X, = . For instance, Graham (2006a) estimates a restricted form of

equation 3, with γju=0 ∀ j, reflecting the assumption of Hicks neutrality. The added

assumption of homogeneity (as in Graham 2005a) results in the familiar Cobb-Douglas

specification, with γhj=0 ∀ h and j. The chosen functional form of the production function can

be applied to the relationship between gross output and productive inputs (a gross output

production function), or between value added and labour and capital inputs (a value added

production function). The following table summarises the relationship between relevant

measures of production, and shows the structure of a gross output production function (h())

and a value added production function (v()):


14

Table 3.1: Gross-output and value-added production functions

Value Added

Gross Output Intermediate Consumption

Labour Costs + Capital Charges +Indirect Taxes + Net Surplus

= +

⎡ ⎤⎢ ⎥⎣ ⎦1 4 4 4 4 4 4 4 4 2 4 4 4 4 4 4 4 4 3

(Equation 4)

Gross output production function

Gross output = h(agglomeration, intermediates, labour, capital)

Value added production function

Gross output = intermediates+ v(agglomeration, labour capital)

Value added = v(agglomeration, labour, capital)

We use the gross output specification because it is more general and, unlike the value added

function, allows for possible substitutability between intermediate consumption and other

factors. The gross output specification also has the advantage that we do not have to exclude

enterprises with negative value added (the log function is undefined for non-positive

numbers), avoiding the selection bias that that would entail.

3.1 Estimation

We estimate agglomeration elasticities using longitudinal microdata on enterprises.

Estimation is based on the following estimating equation, which is a form of equation 3,

augmented with an appropriate error structure:

( )

J H Jj h j

it i u it hj itit itj h j

Jj

ju it uu it ititj

it i t it

Y X U X X

X U U e

e

01 1 1

2

1

1log log log log log

2

1log log log

2

α α γ γ

γ γ

λ τ ε

= = =

=

= + + +

+ + +

= + +

∑ ∑∑

∑ (Equation 5)

Many of our estimates of agglomeration elasticities are based on restricted versions of

equation (5). Our initial regression estimates in table 5.1 are based on a Hicks-neutral variant

(γju=0 ∀j≠u), with linear rather than quadratic agglomeration effects (γuu=0). The production

function parameters are also initially constrained to be common for all industries, yielding an

aggregate production function. We subsequently allow each two-digit industry to have a

distinct production function, while still constraining the agglomeration elasticity to be

common across industries. This is implemented in two stages. First, we estimate the industry-

specific production function, omitting the effective density terms. In the second stage, multi-

factor productivity (the residuals from the first-stage regressions) is regressed on the

effective density term(s). To obtain separate agglomeration elasticity estimates for one-digit

industries and for regions, we interact the effective density measures with industry or region

dummies in the second stage. Finally, in section 5.4, we estimate an unrestricted version of

equation 5 separately for each one-digit industry to examine the extent to which effective

density interacts with other inputs in its impact on productivity.

The assumed error structure also varies across our specifications. All specifications include

year effects (τt) in addition to the white-noise errors (εit). The term λi represents an enterprise-

specific productivity component that is potentially correlated with the productive inputs and

3 Methods

15

effective density. We present a baseline specification, which we refer to as ‘pooled’, that does

not control for enterprise heterogeneity (λi = 0). Failing to control for this heterogeneity will

lead to biased parameter estimates. Estimated agglomeration elasticities will be overstated if

firms with high idiosyncratic productivity are disproportionately located in areas with high

effective density. Such firms would be more productive wherever they operate and we do not

want to count the influence of this heterogeneity as an impact of effective density.

Controlling for enterprise heterogeneity removes the bias and reveals the firm-level

association between changes in effective density and changes in productivity. This is the

relationship that is most relevant for the appraisal of transport proposals that may raise

effective density.

We consider two treatments of firm heterogeneity. First, we include a full set of enterprise

fixed effects, to give estimates that we refer to as ‘within enterprise’. The difficulty with this

approach is that effective density is highly persistent over time, so that including firm fixed

effects essentially removes much of the variation in density. The inclusion of fixed effects can

lead to pronounced attenuation bias (bias towards zero) and imprecisely estimated

coefficients. These problems are exacerbated for small industries or industries that are highly

geographically concentrated, in which case the time-variation in effective density is largely

absorbed by the time effects.

Our second treatment of enterprise heterogeneity is to control for it at a group level.

Specifically, we include dummy variables for each local industry (combination of two-digit

industry and geographic region), to generate estimates that we refer to as ‘within local

industry’. This will remove the influence of higher productivity firms sorting into higher-

density regions. The agglomeration elasticity estimates will still, however, reflect the bias

from any sorting that occurs within regions. These estimates represent a tradeoff between

controlling for the possible endogeneity of effective density and avoiding the attenuation of

the enterprise fixed effects estimates.

Other specification and estimation issues that arise in the estimation of equation 5 include

the endogeneity of productive inputs, and the dynamics of agglomeration effects. A firm’s

choice of inputs may depend on productive characteristics that are unobserved by the

econometrician, and hence are captured in the error term, but are known to the firm. This

would induce a problematic correlation between covariates and the error term eit. Various

methods have been proposed to deal with this simultaneity, including fixed effects, various

instrumental variables approaches, and the use of variables such as measures of investment

behaviour or firm survival that are assumed to be related to the firm’s idiosyncratic

productivity (Griliches and Mairesse 1998; Olley and Pakes 1996).

If the relationship between effective density and productivity operates with a lag (density

changes this year are not reflected in firm performance until next year), enterprise fixed effects

estimates will underestimate the long-run impact of effective density on productivity, which is

captured by pooled estimates. Enterprise fixed effects estimates may also fail to control

adequately for the endogeneity of effective density if short run fluctuations in productivity lead

to short run movements in density. This is likely to be a problem for industries such as

construction, for which productivity and density rise and fall together in response to building

cycles. For such industries, enterprise fixed effects estimates will overstate the strength of the

causal relationship from effective density to productivity. Finally, enterprise fixed effects do not

adequately control for variation across time in unobserved firm-level productivity

characteristics, and tend to magnify the influence of other forms of mis-specification such as

measurement errors and errors in variables (Griliches and Mairesse 1998).


16

On balance, we anticipate that ‘within enterprise’ estimates will understate true

agglomeration elasticities and that ‘within local industry’ estimates will still be somewhat

overstated due to sorting within regions. The tradeoff between bias and sample variability

will have the greatest impact on estimates for smaller industries or regions, for which sample

variability will be greatest. For aggregate estimates, the ‘within enterprise’ estimates should

give a more reliable indication of the causal relationship between agglomeration and

productivity.

4 Data: the prototype Longitudinal Business Database

17


The data used in this study are drawn from Statistics New Zealand’s prototype Longitudinal

Business Database (LBD) for 1999 to 2007. The data were accessed in the Statistics

New Zealand Data Laboratory under conditions designed to give effect to the security and

confidentiality provisions of the Statistics Act 1975. The core of the LBD dataset is the

Longitudinal Business Frame (LBF), which provides longitudinal information on all businesses in

the Statistics New Zealand Business Frame since 1999, combined with information from the tax

administration system. The LBF population includes all economically significant businesses.3

The LBF contains information at both the enterprise level and the plant level. At any time, an

enterprise will contain one or more plants, and each plant will belong to only one enterprise.

Our unit of analysis is the enterprise, although as described below, we use information on

plant locations to obtain measures of effective density for each location where the enterprise

operates. Plants are assigned a ‘permanent business number’ (PBN) that identifies them

longitudinally. The longitudinal links are established through the application of a number of

continuity rules that allow PBNs to be linked even if they change enterprises or tax identifier

(Seyb 2003; Statistics New Zealand 2006). The LBF provides monthly snapshots of an

enterprise’s industry, institutional sector, business type, geographic location and employee

count.4 For PBNs, there is monthly information on industry, location and employee count.

The LBD is a research database that includes the LBF as well as a range of administrative and

survey data that can be linked to the LBF. The primary unit of observation in the LBD is an

enterprise observed in a particular year. The current study uses business demographic

information from the LBF, linked with financial performance measures (from the Annual

Enterprise Survey and various tax returns, including IR10s), and measures of labour input

(working proprietor counts from IR10 forms, and employee counts for PBNs from PAYE (pay-

as-you-earn income tax) returns as included in the Linked Employer-Employee Dataset (LEED).

Gross output and factor inputs are measured in current-prices.5 The primary source used to

obtain a value added measure is the Annual Enterprise Survey (AES). The AES is a postal

sample survey, supplemented with administrative data from tax sources. We use postal

returns from AES to provide annual gross output and factor inputs for each enterprise’s

financial year. This information is available for around 10% of enterprises, which are

disproportionately larger firms, accounting for around 50% of total employment in

3 A business is economically significant if it a) has annual goods and services tax (GST) turnover of

greater than $30,000; or b) has paid employees; or c) is part of an enterprise group; or d) is part of a GST

group; or e) has more than $40,000 income reported on tax form IR10; or f) has a positive annual GST

turnover and has a geographic unit classified to agriculture or forestry.

4 Institutional sector distinguishes producer enterprise; financial intermediaries; general government;

private not-for-profit serving households; households; and rest of the world.

5 Changes over time in current price inputs and outputs will reflect both quantity and price changes. The

use of double deflation to isolate quantity adjustment over time at the industry level is possible using the

Statistics New Zealand PPI input and output indices but only for a selection of one-digit and two-digit

industries. Measures of productivity premia for firms within the same industry will reflect both quantity

and relative price differences. Spatial price indices are not available for the separate identification of

quantity differences.


18

New Zealand. Where AES information is not available, we derive comparable measures from

annual tax returns (IR10s). The methods used for derivation are detailed in Appendix A.

4.1 Production function variables

Gross output is measured as the value of sales of goods and services, less the value of

purchases of goods for resale, with an adjustment for changes in the value of stocks of

finished goods and goods for resale. Enterprise total employment comprises the count of

employees in all of the enterprise’s plants, annualised from employee counts as at the 15th

of each month, plus working proprietor input, as reported in tax returns. Capital input is

measured as the cost of capital services rather than as the stock of capital. There are three

components to the cost of capital services: depreciation costs; capital rental and leasing

costs; and the user cost of capital. The inclusion of rental and leasing costs (including rates)

ensures consistent treatment of capital input for firms that own their capital stock and firms

that rent or lease their capital stock. The user cost of capital is calculated as the value of total

assets, multiplied by an interest rate equal to the average 90-day bill rate plus four

percentage points, to approximate the combined cost of interest and depreciation.

Intermediate consumption is measured as the value of other inputs used up in the production

process, with an adjustment for changes in stocks of raw materials.

4.2 Effective density

Effective density is calculated for each area unit6, based on plant level employment, using

information on all plants, and is calculated using equation (2), with the distance decay (α) set

to equal 1. Monthly labour input for each PBN is calculated as the sum of rolling mean

employment (RME) plus a share of working proprietor input in the enterprises to which the

PBN belongs. RME is the average number of employees on the PBN’s monthly PAYE return in

the 12 months of the enterprise’s financial year, as recorded in the LEED data. PAYE

information is not always provided at the PBN level, and in LEED, there is some allocation of

PAYE information to PBNs as outlined in Seyb (2003). The annual number of working

proprietors in each enterprise is available in the LEED data, based on tax return information.

Labour input from working proprietors is allocated to the PBNs within each enterprise in

proportion to the PBN’s RME. Where an enterprise has only working proprietors, the working

proprietor input is allocated equally across all component PBNs. There is a large number of

PBNs in each year for which RME is zero. The log of labour input is undefined for these PBNs

unless working proprietor information is also incorporated. Using working proprietor

information increases the number of plants with usable labour productivity information by

80% to 100%, and increases measured aggregate labour input by 13% to 20%.7

6 An area unit is a geographical area with an average size of around 140 square kilometres and

employment of roughly 1000. In urban areas, the areas are much smaller and the employment counts

somewhat higher. For instance, area units in the Auckland region are on average around 13 square

kilometres and contain employment of about 1500. In Auckland City, they have an average area of 5.5

square kilometres and employment of 2500.

7 The increases due to working proprietor inclusion decrease monotonically over time. The contribution

to the number of plants (to labour input) are 103% (20%) in 2000, and 79% (13%) in 2006. The impacts

are particularly pronounced in single-PBN enterprises that do not belong to an enterprise group. In 2006,

the impacts were 101% (24%) and in 2000 they were 142% (37%). There will be some double counting of

working proprietors if they also draw PAYE earnings, as they will also appear in the rme employee count.


19

For enterprises that have employing plants in more than one area unit, a separate observation

is included for each plant. The enterprise production function variables are repeated across

the observations but a separate effective density measure is calculated for each location. All

estimation is carried out allowing for clustering of errors at the enterprise level, to reflect the

resulting correlation in errors. The multiple observations are weighted by the proportion of

enterprise employment in each location, so that the sum of weights across the separate plant

observations is one for each enterprise.8

For each year from 1999/2000 to 2005/06 (referred to as 2000 to 2006 respectively for the

remainder of the paper), we select enterprises plants that a) are always private-for-profit; b)

are never a household or located overseas; c) have non-missing industry information; and d)

are not in the ‘government administration and defence’ industry.9 We exclude plants for

which location (area unit, territorial authority, or regional council) information is missing, and

plants in area units outside territorial authorities (island and inlets). In order to maintain a

consistent population that can support analysis while protecting confidentiality, some

additional exclusions10 are applied. Finally, we drop observations where labour input is zero.

Table 4.1 displays summary statistics for our analysis sample. There are 886,700 enterprise-

year observations. Average effective density for the enterprises is 30,248, with a range of

2298 to 172,863. This range is considerably lower than is observed in the United Kingdom.

The minimum effective density observed in the United Kingdom in 2002 (29,515) is around

the New Zealand mean, and the New Zealand maximum effective density is well below the

United Kingdom mean of 224,132 (Graham 2006b, p 103). The second and third columns of

table 4.1 show the rise in effective densities over our study period, reflecting both a general

increase in employment and a slight increase in concentration of economic activity. Summary

statistics are also provided for the log of effective density and the square of the log. These

are the variables that are used in estimation.

8 The approach here differs from that in Graham and Kim (2007), who exclude multi-plant firms from

their analysis, though noting the inherent problem of dealing with multi-plant firms – ‘Even if we had

data on the production characteristics at each individual plant, the fact that these form part of a wider

corporation weakens the imposition of assumptions about optimization at the plant level’ (p 274). The

inclusion of multi-plant enterprises also provides more generalisable results.

9 Formally, these restrictions refer to a) business type 1-6 (individual proprietorship, partnership, limited

liability company, co-operative company, joint venture and consortia, branches of companies

incorporated overseas); b) Institutional Sector is never ‘household’ or ‘located overseas’ and ANZSIC

industry is not Q97 (households employing staff); c) ANZSIC division M.

10 Specifically, we exclude area units in the Chatham Islands, the Middlemore area unit in Auckland

(521902), and six Auckland area units that are tidal, inlets or islands (615900, 616001, 617102,

617702, 617903, 617604). Tidal areas of Waiheke Island (AU 520804) are grouped with Waiheke Island

itself.


20

Table 4.1: Summary statistics

Pooled 2000 2006

Mean

Standard

deviation Mean

Standard

deviation Mean

Standard

deviation

Effective density 30,248 (31,107) 27,106 (28,300) 33,289 (33,343)

(range) [2,298–172,863] [2,298–150,885] [2,651–172,863]

ln(eff.dens) 9.87 (0.94) 9.76 (0.93) 9.97 (0.94)

(range) [7.74–12.06] [7.74–11.92] [7.88–12.06]

ln(eff.dens) squared 98.32 (18.81) 96.15 (18.52) 100.35 (19.00)

ln(gross output) 11.68 (1.68) 11.48 (1.66) 11.85 (1.69)

ln(intermed.cons) 10.64 (1.83) 10.37 (1.81) 10.84 (1.83)

ln(employment) 0.85 (1.01) 0.85 (0.97) 0.86 (1.06)

ln(capital services) 9.92 (1.68) 9.87 (1.61) 10.03 (1.76)

Data sourced from AES 0.06 (0.23) 0.06 (0.23) 0.06 (0.25)

ln(cap.serv) squared 101.28 (33.21) 99.99 (31.49) 103.63 (35.23)

ln(cap.serv)*ln(emp) 9.46 (12.57) 9.29 (11.94) 9.74 (13.34)

ln(cap.serv)*ln(intcons) 107.34 (33.30) 103.83 (31.41) 110.67 (34.93)

ln(cap.serv)*ln(effdens) 97.84 (18.82) 96.23 (17.99) 99.87 (19.64)

ln(emp)*ln(emp) 1.74 (3.72) 1.65 (3.55) 1.86 (3.93)

ln(emp)*ln(intcons) 10.25 (13.92) 9.93 (13.26) 10.60 (14.71)

ln(emp)*ln(effdens) 8.53 (10.45) 8.38 (9.97) 8.71 (11.04)

ln(intcons)*ln(intcons) 116.65 (40.40) 110.84 (39.05) 120.96 (41.27)

ln(intcons)*ln(effdens) 105.20 (21.83) 101.50 (21.95) 108.22 (21.75)

Observations 886,700 133,900 118,100

Labour share of cost 0.42 (0.23) 0.42 (0.22) 0.42 (0.24)

Intcons share of cost 0.37 (0.22) 0.35 (0.22) 0.38 (0.22)

Capital share of cost 0.21 (0.19) 0.23 (0.21) 0.20 (0.19)

Observations with labour share>0 788,200 119,000 104,700

Source: Statistics New Zealand prototype Longitudinal Business Database. Observation counts represent

enterprise-year observations and are randomly rounded to the nearest 100, which is greater than is

required by Statistics New Zealand’s rules for non-disclosure.

The second block of table 4.1 summarises gross output and factor inputs. The mean of the

log of gross output is 11.68, which corresponds to (geometric) average gross output of

$118,200. Mean log intermediate consumption and log capital services are 10.64 ($41,800)


21

and 9.92 ($20,300) respectively. Mean log employment is 0.85, which corresponds to 2.3

full-time equivalent employees. Employment is the only pure quantity measure here. Changes

over time in output, intermediate consumption and capital services reflect a combination of

price changes. Subsequent regression analysis controls for period effects to allow for general

price increases. An implication of the use of current-value input and output measures is that

measured productivity differences; across time, across industries, or across locations, reflect

allocative as well as technical productivity differences. Operating in time periods, industries,

or locations where output prices are high relative to input prices is, by this measure, more

productive.

Around 6% of observations use data from AES, with the remainder based on IR10 tax forms.

Table 4.1 also presents means of interaction variables that are included in translog

production function regressions. These are included to aid in the interpretation of

coefficients, rather than having any ready interpretation per se.

The final panel shows cost shares for labour, capital and intermediate consumption. Labour

costs are measured as total labour earnings from LEED. This includes both wage and salary

earnings, and the earnings of the self-employed. In many cases, reported self-employed

earnings are zero or negative, leading to potentially negative labour cost shares. The

reported cost shares are thus based on a sub-sample of enterprises that excludes those with

non-positive labour earnings. In all three years, labour costs account for 42% of total costs,

intermediate consumption for 35% to 38%, and capital costs the remaining 20% to 23%.


22

5 Results

5.1 Aggregate estimates

Table 5.1 presents regression estimates of agglomeration elasticities a Hicks-neutral translog

production function specification.11 The first column shows an agglomeration elasticity of

0.171. This implies that firms in locations with 10% higher effective density have productivity

that is 1.7% higher. This estimate makes no adjustment for enterprise heterogeneity and

sorting. Controlling for productivity and density differences across regions and industries

reveals that around 70% of the cross-sectional relationship between effective density and

productivity is attributable to observable differences in regional industry composition. The

estimated elasticity is reduced to 0.048, as shown in column 2.12

Table 5.1: Agglomeration elasticities: Hicks-neutral translog production function specification

Aggregate production function Industry production functions

Pooled

(1)

Within local

industry

(2)

Within

enterprise

(3)

Pooled

(4)

Within local

industry

(5)

Within

enterprise

(6)

Linear agglomeration effects

ln(effdens) 0.171** 0.048** 0.015** 0.037** 0.069** 0.010*

[0.001] [0.003] [0.005] [0.001] [0.003] [0.005]

Quadratic agglomeration effects

ln(effdens) 0.360** -0.088* -0.402** -0.200** -0.007 0.184**

[0.029] [0.042] [0.071] [0.024] [0.038] [0.070]

ln(effdens) squared -0.009** 0.007** 0.020** 0.012** 0.004* -0.009*

[0.001] [0.002] [0.003] [0.001] [0.002] [0.003]

Notes: Robust standard errors clustered at the enterprise level. **: significant at 1%; *: significant at 5%.

See Appendix table 1 for full regression estimates for the aggregate production function specifications.

The third column of table 5.1 controls more fully for enterprise composition differences, by

including enterprise fixed effects. This has the effect of removing the influence of observable

and unobservable differences in enterprise productivity and location that are constant over

time (including industry). For single plant enterprises, the estimates reflect the relationship

between enterprise productivity and the changing effective density in their location. For

multi-plant enterprises, it also reflects the effect of changes in the firm’s share of

employment in each location. It is plausible that such changes may be made endogenously,

with enterprises choosing to increase their presence in areas where their productivity is

higher. This form of endogeneity will lead to an upward bias in the estimated elasticity. The

impact of controlling for enterprise fixed effects is to reduce the estimated elasticity by over

11 Appendix table 1 shows estimates of production function parameters for the specifications shown in

Table 5.1.

12 Controlling for industry composition alone reduces the coefficient to 0.041.

5 Results

23

90%; from 0.171 to 0.015. The lower precision of the fixed effects estimates is evident in the

size of the standard errors on the fixed effects coefficients. The standard error on the

agglomeration elasticity is 0.005, around five times the size of the standard error on the

pooled coefficient (0.001) in the first column. Appendix table 1 shows the other coefficients

in the aggregate production function estimation. In contrast to the impact of fixed effects

estimation on the agglomeration elasticity standard errors, the standard errors on the other

production function coefficients do not change markedly, reflecting greater within-enterprise

variability to support identification.

In columns 4 to 6 of table Table 5.1, we show the corresponding estimates of agglomeration

elasticities obtained when we relax the constraint that production function parameters are

common across industries. The pooled estimates shown in column 4 show an agglomeration

elasticity of 0.037. Controlling for the local-industry composition of enterprises leads to a

higher estimated elasticity (0.069), implying that, within industries, more productive firms are

disproportionately located in lower density areas. It would appear that the pooled estimates

over-estimate the productivity impact of agglomeration, suggesting concerns that

composition bias resulting from the sorting of enterprises between locations inflates

agglomeration elasticity estimates is unfounded.

The small difference between the pooled and ‘within local industry’ estimates using industry-

specific production functions suggests the bias arising from endogenous density may be

relatively small.13 In contrast, imposing a common production function across all industries,

as in the upper panel of figure 5.1 and the first three columns of table 5.1, yields a stark

difference between pooled and ‘within local industry’ estimates, pointing to the invalidity of

the assumption of common technologies. Agglomeration elasticities based on aggregate

production functions should, at a minimum, control for heterogeneity across local industries

to allow for this mis-specification.

The ‘within enterprise’ specification shown in column 6 yields a low estimated elasticity of

0.010. We are not able to distinguish whether this reduction is a consequence of the sorting

of more productive enterprises into denser areas within regions, or of the attenuation bias

associated with the use of enterprise fixed effects.

The agglomeration elasticity estimates obtained when we relax the constraint of a linear

relationship are shown in the lower panel of table 5.1. To aid the interpretation of the

coefficients, we plot the implied relationship between density and productivity in figure 5.1.

The upper panel shows the relationship between effective density and productivity based on an

aggregate production function. The three solid curves correspond to the first three columns of

table 5.1, with the corresponding linear relationships shown by broken lines. The steepest line

reflects the pooled estimate, with a corresponding linear coefficient of 0.171. The ‘within local

industry’ relationship is less steep. The ‘within enterprise’ line shows a downward slope, and

thus negative agglomeration elasticities, at lower densities. Both the ‘within local industry’ and

‘within enterprise’ profiles show increasing returns to agglomeration.

Panel (b) of figure 5.1 shows agglomeration elasticities based on industry-specific production

functions. Consistent with the linear elasticity estimates in table 5.1, the slope of the pooled

estimates is slightly lower than the ‘within local industry’ estimates, though relatively similar.

13 It may also be that firms that benefit most from density (rather than firms that have higher

productivity per se) sort into more dense areas. In this case, the agglomeration elasticity obtained from

the ‘within local industry’ estimates provide a relevant measure of the likely causal impact of changing

density.


24

The ‘within enterprise’ estimates are again very flat and slightly negative at higher densities.

The pooled and ‘within local industry’ estimates show slight increasing returns to

agglomeration, though the curves are fairly close to the corresponding linear profiles.14

(a) Aggregate production function

11.50

11.55

11.60

11.65

11.70

11.75

11.80

11.85

11.90

8 8.5 9 9.5 10 10.5 11 11.5 12ln(Effective Density)

Pre

dict

ed ln

(Gro

ss O

utpu

t)

Within Local Industry

Within Enterprise

Pooled

(Interquartile )

(b) Industry-specific production functions

11.50

11.55

11.60

11.65

11.70

11.75

11.80

11.85

11.90

8 8.5 9 9.5 10 10.5 11 11.5 12ln(Effective Density)

Pre

dict

ed ln

(Gro

ss O

utpu

t)

Within Local Industry

Within Enterprise

Pooled

(Interquartile range)

Figure 5.1: Agglomeration profiles

Note: The productivity-density profiles are those implied by the quadratic coefficients shown in table 5.1.

Broken lines show the corresponding linear elasticity estimates.

The reliability of the estimates depends on the validity of the various assumptions and

constraints. First, the assumption that factor choices and effective density is exogenous,

14 Graham 2007 allows for a quadratic relationship using cross-sectional United Kingdom data and finds

diminishing returns to agglomeration.

5 Results

25

conditional on included co-variates, can be questioned. We were unable to find satisfactory

ways of controlling for possible endogeneity.15 Second, the assumption that the effect of

effective density is Hicks-neutral can also be relaxed. As discussed in section 5.2, relaxing

this assumption does not change the agglomeration elasticity estimates, when evaluated at

sample means, but does provide more information on the nature of factor augmentation and

price effects.

5.2 Estimates by one-digit industry

Table 5.2 presents estimates of equation (5) that allow for industry-specific production

coefficients for each two-digit industry. Separate agglomeration elasticities are estimated by

one-digit industry.16 The reported coefficients are for a linear effective density specification.

The first column of agglomeration elasticities, labelled ‘NZTA’, are the existing estimates

from NZTA (2008), derived from United Kingdom agglomeration elasticities. These are shown

for United Kingdom industry groupings, which do not correspond exactly with New Zealand

one-digit groups. Corresponding estimates of New Zealand agglomeration elasticities are

positive and significant for all industries except for the mining and quarrying group (B),

where the estimate is insignificant.

Table 5.2: Agglomeration elasticities by one-digit industry

Industry-specific production

functions

NZ industry

Number of

enterprises UK industry

NZTA

(1)

Within

Industry

(2)

Within

local

industry

(3)

Within

enterprise

(4)

A Agriculture, forestry and

fishing 63,200

0.013**

[0.003]

0.032**

[0.003]

0.041**

[0.005]

B/D Mining and electricity,

Gas and water 320

0.024

[0.020]

0.035*

[0.016]

0.012

[0.009]

C Manufacturing 20,000 Manufacturing 0.024 0.049**

[0.002]

0.061**

[0.003]

0.016**

[0.005]

E Construction 34,100 Construction 0.088 0.039**

[0.002]

0.056**

[0.003]

0.011*

[0.005]

15 We attempted to use instrumental variables methods to test for and correct for possible endogeneity

but could not identify suitable instruments. Lagged levels of inputs and density consistently failed

overidentification tests. In the light of this finding, we also examined possible dynamic relationships,

estimating a differenced equation with a lagged dependent variable. We tried to instrument for the

lagged dependent variable, and also for factor choice and density using suitable lags. We were unable to

find suitable lags that passed standard tests of overidentification, making our estimates uninterpretable.

The combination of differencing and instrumenting also reduced the number of usable observations by

more than 50%. On balance, we believe that controlling for firm-level heterogeneity through the use of

enterprise fixed effects leads to more appropriate estimates than are obtained from pooled estimates.

However, problems of endogeneity may remain, which we would expect to bias upwards our estimates of

agglomeration elasticities. The potential endogeneity also makes the investigation of dynamics

problematic.

16 Industry group D (electricity, gas and water) has been omitted to prevent disclosure. Industry groups

M (public administration and defence) Q (personal and other services) and R (not elsewhere classified)

have been omitted.


26

Industry-specific production

functions

NZ industry

Number of

enterprises UK industry

NZTA

(1)

Within

Industry

(2)

Within

local

industry

(3)

Within

enterprise

(4)

F Wholesale trade 13,200 0.072**

[0.002]

0.086**

[0.003]

0.018**

[0.005]

G Retail trade 34,200 0.065**

[0.002]

0.086**

[0.003]

0.027**

[0.005]

H Accommodation, cafes

and restaurants 10,500

Distribution,

hotels and

catering

0.044

0.041**

[0.003]

0.056**

[0.004]

0.030**

[0.005]

I Transport and storage 9,800 0.041**

[0.003]

0.057**

[0.004]

0.014**

[0.005]

J Communication services 2,800

Transport, storage

and

communications

0.049 0.053**

[0.005]

0.068**

[0.006]

0.001

[0.006]

K Finance and insurance 3,200 Banking, finance

and insurance 0.180

0.076**

[0.006]

0.087**

[0.006]

-0.006

[0.006]

Real estate 0.084

IT 0.082 L Property and business

services 56,500

Business services 0.167

0.074**

[0.002]

0.079**

[0.003]

0.000

[0.005]

M

Government

administration and

defence

Public services 0.292

N Education 1,800 0.076**

[0.008]

0.076**

[0.008]

0.022**

[0.008]

O Health and community

services 9,900

0.047**

[0.005]

0.083**

[0.006]

-0.009

[0.006]

P Cultural and recreational

services 1,200

0.062**

[0.010]

0.053**

[0.009]

0.004

[0.010]

Weighted average* 250,800 0.127 0.049 0.065 0.019

All industries 250,800 0.037**

[0.001]

0.069**

[0.003]

0.010*

[0.005]

* Weighted averages are calculated using industry employment shares for the NZTA estimates, and using

shares of enterprise-year observations for the other columns.

Comparing the NZTA and pooled estimates for industries that are covered in both columns,

the NZTA estimates are generally reassuringly similar – perhaps surprisingly given that the

former were based on United Kingdom estimates in an ad hoc manner, adjusted to allow for

significant differences in densities. Overall, the weighted mean agglomeration elasticity is,

however, much smaller for the pooled column, reflecting the inclusion of low-elasticity

industry groups that were excluded from the NZTA estimates, and the exclusion of the high-

elasticity public administration and defence industry from the pooled estimates.

As was the case for the overall estimates in table 5.1, controlling for sorting of enterprises

across local industries leads to generally higher estimated agglomeration elasticities, with the

only exceptions being the relatively small education and cultural and recreational services

5 Results

27

industries. The impact of controlling for enterprise fixed effects is to give lower estimates,

with the exception of agriculture, forestry and fishing. Agglomeration elasticity estimates

become insignificant in six industries, including the finance and insurance industry, which

has the largest estimated elasticity in column (3). The reduction in estimated elasticities

probably reflects the consequent imprecision of the enterprise fixed effects estimates rather

than sorting alone.

On balance, we believe that the ‘within local industry’ estimates in column (3) provide the

best indication of industry-specific agglomeration elasticities. While they are probably biased

by the sorting of high productivity firms into areas it is not clear how large the bias is, or

even the direction of bias. The fact that controlling for sorting between regions increases

estimated elasticities suggests that composition bias may be negative.

5.2.1 Non-linear agglomeration effects

Table 5.2 summarises agglomeration elasticities under the assumption of a linear

relationship between density and productivity, from the ‘within local industry’ specification.

In figure 5.2, we show the productivity-density profiles implied by quadratic agglomeration

elasticity estimates. For ease of presentation, the industry groups are divided into two sets.

The top panel of figure 5.2 shows the agglomeration profiles for six industries characterised

by high average effective density and high agglomeration elasticities. These are industries

with average density greater than 10.2, and include the industries with the five highest

‘within local industry’ agglomeration elasticities in column (3) of table 5.2. The profiles are

plotted so that each industry’s profile crosses zero at the industry’s mean ln(effective

density). Mean density and output are also shown in brackets next to the industry’s name.

Each profile is plotted only for densities between the 10th and 90th percentile of effective

density for the industry.

The slopes of these profiles are positive for all industries except agriculture, forestry and

fishing, and the combined mining and quarrying, and electricity, gas and water industries.

The profiles show decreasing returns to effective density for all industries. Agglomeration

elasticities are shown by the slopes of the profiles. In figure 5.3, we plot the agglomeration

elasticities that are implied by the figure 5.2 profiles. Because of the imposed quadratic

functional form, these agglomeration elasticity plots are linear. Because of decreasing returns

to agglomeration, all slope downwards.

Relatively high agglomeration elasticities are evident for five industries: property and

business services, finance and insurance, communication services, cultural and recreational

services, and education. Evaluated at overall average density of 9.87, the agglomeration

elasticities are 0.16, 0.13, 0.12, 0.09, and 0.08 respectively. With the exception of the

primary industries, all others show moderate elasticities that are similar to each other, and

vary from 0.04 to 0.07 at the overall average density of 9.87.

One key feature highlighted by the comparison of figure 5.2 with figure 5.3 is that, even

though productivity is higher in denser areas, the additional gain from further increases in

density is smaller in denser areas. One implication of these patterns is that the impact of

agglomeration on productivity will vary across different regions for two reasons. First, for a

given industry structure, agglomeration elasticities will be smaller in denser areas as a result

of decreasing returns. Second, denser areas are likely to have a disproportionate share of

enterprises that benefit most from agglomeration. Such industries include property and

business services and finance and insurance, the high agglomeration elasticities for which are

evident in figure 5.3. It is an empirical question which of these factors dominates.


28

High-density Industries

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

8.00 8.50 9.00 9.50 10.00 10.50 11.00 11.50 12.00ln(Effective Density)

Pro

duct

ivity

Pre

miu

m

(cro

sses

zer

o at

mea

n de

nsity

)

Cultural and Recreational Services (10.66,11.64)

Property & Business Services (10.32,11.45)

Finance and Insurance (10.66,12.47)

Education (10.34,11.62)

Wholesale Trade (10.41,12.31)

Other Industries

-0.30

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20


Pro

duct

ivity

Pre

miu

m

(cro

sses

zer

o at

mea

n de

nsity

)

Communication Services (10.03,11.17)

Construction (9.94,11.76)

Accommodation, Cafes & Restaurants (9.89,12.15)Transport and Storage (10.02,12.02)

Retail Trade (10.10,11.55)Manufacturing (10.15,12.53)

Health & Community Services (10.26,11.96)

Agriculture, Forestry and Fishing (9.06,11.31)

Mining, EG&W (9.15,13.13)

Numbers in brackets show (mean ln(effective density), mean ln(gross output))

Figure 5.2: Productivity profiles – industry-specific regressions

5 Results

29

High-density Industries

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25


Agg

lom

erat

ion

Ela

stic

ity

Cultural and Recreational Services (10.66,11.64)

Property & Business Services (10.32,11.45)

Finance and Insurance (10.66,12.47)

Education (10.34,11.62)

Wholesale Trade (10.41,12.31)

Other Industries

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25


Agg

lom

erat

ion

Ela

stic

ity

Communication Services (10.03,11.17)Construction (9.94,11.76)

Accommodation, Cafes & Restaurants (9.89,12.15)Transport and Storage (10.02,12.02)

Retail Trade (10.10,11.55)Manufacturing (10.15,12.53)

Health & Community Services (10.26,11.96)

Agriculture, Forestry and Fishing (9.06,11.31)

Mining, EG&W (9.15,13.13)

Numbers in brackets show (mean ln(Effective density), mean ln(gross output))

Figure 5.3: Agglomeration elasticities – industry-specific regressions

5.3 Estimates by region

In this section, we present estimates of agglomeration elasticities by region, to gauge

whether cross-region differences in agglomeration elasticities are dominated by decreasing

returns or by high-density regions attracting a disproportionate share of industries (or

enterprises) that benefit most from agglomeration. We present estimates for each regional

council area, with West Coast, Marlborough, Tasman and Nelson combined. For the Auckland


30

region, we also present separate estimates for each of the territorial authorities within

Auckland.

Table 5.3 summarises the results. The number of enterprise-year observations is shown in

column (1). The mean density of each area is shown in column (2). The estimates in column

(3) are obtained by regressing multi-factor productivity on a full set of location dummies and

their interactions with ln(effective density).17

Controlling for local industry composition, as shown in column (4), lowers the estimated

agglomeration elasticities for high-density regions - all those with ln(effective density) greater

than 9.9 (Canterbury), and raises estimated elasticities for low-density regions. This implies

that, within high-density regions, more productive industries sort into higher-density areas.

If, in addition, there is, within industry sorting of more productive firms into higher-density

areas, the ‘within local industry’ estimates for these regions, shown in column (4), will be

biased upwards. For low-density regions, the opposite pattern holds - more productive

industries appear to sort away from the high-density areas.

Table 5.3: Agglomeration elasticities – differences across regions

Industry production function

Number of

observations

(000)

(1)

ln(eff dens)

(2)

Within

locality

(3)

Within local

industry

(4)

Within

enterprise

(5)

Northland region 41.0 9.07 0.119** 0.177** 0.051

[0.012] [0.013] [0.038]

Auckland region 223.8 10.98 0.076** 0.056** -0.033*

[0.008] [0.008] [0.014]

Rodney 22.2 9.93 0.145** 0.088** -0.009

[0.027] [0.029] [0.053]

North Shore 39.3 10.96 0.023 0.020 -0.093*

[0.025] [0.026] [0.042]

Waitakere 23.5 10.78 0.017 -0.010 -0.068

[0.036] [0.037] [0.064]

Auckland city 87.0 11.44 0.071** 0.061** -0.027

[0.009] [0.010] [0.016]

Manukau 35.1 10.86 0.099** 0.055 -0.036

[0.031] [0.030] [0.041]

Papakura 6.3 10.48 0.109 -0.006 0.050

[0.072] [0.069] [0.124]

Franklin 10.4 10.03 0.100 -0.016 -0.002

17 The separate estimates for the areas within Auckland were obtained by running a separate regression

with the Auckland region dummy replaced by separate dummies for the territorial authorities. The

coefficients on other regions were, of course, identical across the two specifications.

5 Results

31

Industry production function

Number of

observations

(000)

(1)

ln(eff dens)

(2)

Within

locality

(3)

Within local

industry

(4)

Within

enterprise

(5)

[0.110] [0.109] [0.149]

Waikato region 102.9 9.68 0.009 0.088** 0.050*

[0.008] [0.009] [0.021]

Bay of Plenty region 62.7 9.62 0.069** 0.107** 0.00

[0.012] [0.013] [0.028]

Gisborne region 10.0 9.00 -0.001 0.222** 0.051

[0.030] [0.043] [0.082]

Hawke’s Bay region 35.2 9.44 0.042** 0.103** 0.055

[0.013] [0.017] [0.033]

Taranaki region 29.7 9.26 -0.130** 0.076** 0.005

[0.015] [0.019] [0.037]

Manawatu-Wanganui region 55.4 9.40 0.004 0.091** 0.035

[0.009] [0.012] [0.025]

Wellington region 85.5 10.17 0.085** 0.063** 0.016

[0.006] [0.006] [0.011]

West Coast, Tasman, Nelson, Marl 43.8 9.11 0.068** 0.084** 0.049

[0.010] [0.012] [0.031]

Canterbury region 122.3 9.91 0.066** 0.048** 0.014

[0.003] [0.005] [0.011]

Otago region 43.7 8.98 0.041** 0.071** 0.016

[0.006] [0.007] [0.015]

Southland region 30.7 8.58 -0.042** 0.061** -0.017

[0.010] [0.015] [0.036]

The standard errors on the estimated agglomeration elasticities for the ‘within locality’ and

‘within local industry’ columns range from 0.003 to 0.019 for all but seven of the locations.

For the Gisborne region, and for six of the seven territorial authorities in the Auckland region

(the exception is Auckland City), the standard errors are higher, ranging from 0.025 to 0.110.

These areas have relatively low numbers of enterprise-year observations, and, especially for

some of the Auckland territorial authorities, limited variation in effective density, due to the

geographic concentration of employment in relatively small areas. For these locations, the

estimates shown in table 5.3 are an unreliable estimate of the actual elasticity.18 Perhaps not

18 The fragility of the estimates is confirmed by estimating quadratic agglomeration effects (estimates

not shown). For most locations, the slope at means is similar to the linear estimates. For the hard-to-


32

surprisingly, the ‘within enterprise’ estimates are imprecise, and none of the locations has

elasticity estimates that are significant at the 5% level of significance.

The ‘within locality’ ‘within local industry’ estimates in table 5.3 are presented graphically in

figure 5.4, making this pattern more evident. In figure 5.4, regions and territorial authorities

are ordered from lowest to highest effective density. Mean density is plotted as the upward

sloping broken line, plotted against the right-hand axis. The immediate impression from

figure 5.4 is that the relationship between a region’s density and its agglomeration elasticity

is not as systematic as was the case for industries. A less systematic pattern may be expected

due to the interaction of decreasing returns and industry composition, as noted above. The

variability does, however, also reflect the lack of relevant variation in some locations, making

it difficult to identify precisely a statistical relationship.

Interpreting the ‘within local industry’ estimates, we find that the three densest regions,

Auckland, Wellington and Canterbury, have similar agglomeration elasticities of 0.056, 0.063,

and 0.048 respectively. With the exception of Southland (0.061), all other regions have

elasticities of at least 0.07. This is consistent with the decreasing returns to effective density

that was evident in the industry-specific estimates in table 5.2.

identify areas, quadratic profiles are imprecise, with agglomeration elasticities having steeply positive or

steeply negative slopes and passing through zero at around mean density.

5 Results

33

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

SO

UTH

LAN

D R

EG

ION

O

TAG

O R

EG

ION

G

ISB

OR

NE

RE

GIO

N

NO

RTH

LAN

D R

EG

ION

W

ES

T C

OA

ST,

TA

SM

AN

, NE

LSO

N, M

AR

L TA

RA

NA

KI R

EG

ION

M

AN

AW

ATU

-WA

NG

AN

UI R

EG

ION

H

AW

KE

'S B

AY

RE

GIO

N

BA

Y O

F P

LEN

TY R

EG

ION

W

AIK

ATO

RE

GIO

N

CA

NTE

RB

UR

Y R

EG

ION

R

odne

y

Fr

ankl

in

W

ELL

ING

TON

RE

GIO

N

Pap

akur

a

W

aita

kere

Man

ukau

Nor

th S

hore

AU

CK

LAN

D R

EG

ION

A

uckl

and

City

Agg

lom

erat

ion

Elas

ticity

4

5

6

7

8

9

10

11

12

log

of E

ffect

ive

Den

sity

Within locality LinearWithin local ind Linearln(EffDens) (RH scale)

Note: Territorial authorities within Auckland are indicated by a circle. All other points relate to regional

council areas.

Figure 5.4: Agglomeration elasticities – differences across regions


34

5.4 Factor augmenting effects and price effects

In this section, we relax the assumption that effective density has a Hicks-neutral effect on

productivity, and allow for the interaction of effective density with other factors of

production. We estimate an unrestricted version of equation 5 and, using the analytical

framework presented in Graham and Kim (2007), calculate a range of derived measures to

identify key features of the production function and the role of agglomeration. In particular,

Graham and Kim use production theory to decompose the overall agglomeration elasticity

into a direct effect, and the contributions that result from agglomeration altering the

efficiency of other factors of production, by differentiating equation 5 by U:

( ) jitu uu it ju it

it jDirect EffectFactor augmenting

effects

YU X

Ulog

log logγ γ γ

−

∂= + +

∂ ∑1 4 44 2 4 4 431 4 4 2 4 43

(Equation 6)

They also derive expressions for the elasticity of output with respect to each factor of

production (∂logYit/∂logXjit), and the impact of agglomeration on the demand for each factor:

j j jit it it

jit itit

X P P

U UX

1log log log

log loglog

−⎛ ⎞ ⎛ ⎞∂ ∂ ∂⎜ ⎟ ⎜ ⎟=⎜ ⎟ ⎜ ⎟∂ ∂∂⎝ ⎠ ⎝ ⎠

(Equation 7)

where j

itP is the price of input j. Agglomeration thus affects the price of each factor,

according to its impact on factor efficiency. The effect on factor demand then depends on the

factor demand elasticity ( log logjit itP U∂ ∂ ), with a greater change in the amount of a

factor demanded when demand is elastic (ie: when log logj jit itP X∂ ∂ is small). (See Graham

and Kim 2007 for further details.)

Table 5.4 summarises the key measures based on an aggregate production function, the

estimated parameters of which are presented in Appendix table 2. All elasticities are

calculated at sample means of all variables. We present both pooled and ‘within enterprise’

effects estimates, corresponding to the entries in table 5.1.

Table 5.4: Translog estimates – derived relationships

(A) Scale and agglomeration

Returns to

scale

Agglomeration

elasticity =

Labour

augmenting

+ Capital

augmenting

+ Intcons

augmenting

+ Direct

effect

(∂Y/∂U) (γlu*L) (γ

ku*K) (γ

iu*I) (γ

u+γ

uu*U)

Pooled 1.076 0.186 0.030 0.268 -0.979 0.868

WE 1.039 0.012 0.034 0.159 -0.532 0.351

(B) Factor elasticities

Output elasticities Demand elasticities

∂Y/∂X

∂PX/∂U ∂X/∂P

X ∂X/∂U

Capital Pooled 0.129 0.234 -1.321 -0.309

FE 0.191 0.078 -1.208 -0.094

Labour Pooled 0.332 0.129 -1.241 -0.160

5 Results

35

(B) Factor elasticities

Output elasticities Demand elasticities

FE 0.317 0.121 -1.268 -0.153

Intermediates Pooled 0.614 -0.126 -1.157 0.146

FE 0.531 -0.100 -1.201 0.120

The top panel of table 5.4 shows the implied returns to scale, and a decomposition of the

overall agglomeration elasticity. There is evidence of slightly increasing returns scale in both

the pooled (1.076) and ‘within enterprise’ (1.039) specifications. The agglomeration

elasticities for the full translog function, estimated at sample means, are shown in the second

column and are similar to those estimated from the more restricted specification in table 5.1,

with Hicks-neutrality and linearity of agglomeration effects imposed. The pooled estimate of

the agglomeration elasticity at means is 0.186 (0.171 in table 5.1). When enterprise

heterogeneity is controlled for using enterprise fixed effects, the elasticity drops to 0.012

(0.015 in table 5.1).

The remaining columns of table 5.4 decompose the overall agglomeration elasticity into four

additive components: one component for each of the three factors of production, indicating

the extent to which agglomeration raises the efficiency of the factor, and one direct effect.

For the three factor augmentation columns, a positive estimate indicates that the efficiency of

the factor is raised by agglomeration and a negative quantity indicates that the factor is less

efficient in areas with high effective density. In both the pooled and ‘within enterprise’

specifications, effective density is associated with higher efficiency of labour and capital

inputs, and lower efficiency of intermediate consumption. Recall that our measures of

intermediate consumption and capital are based on dollar values rather than pure quantity

indices. The lower efficiency of intermediate consumption in denser areas may thus reflect

higher input prices: the same dollar input adds less to output in denser, high-input-price

areas. However, capital inputs, in particular, land, are also more expensive in denser areas,

yet the efficiency of capital services charges is higher in denser areas despite the possible

price effects. There is a high positive direct effect of agglomeration, indicating that

productivity would be higher in denser areas even holding factor inputs and factor efficiency

constant. The strength of estimated factor augmentation effects is reduced for capital and

intermediate consumption when we control for enterprise fixed effects. This suggests that

there is sorting of firms in more dense areas, with denser areas having firms with more

efficient capital usage and less efficient intermediate consumption usage at the margin.

The second panel of table 5.4 displays the output elasticity of each factor, and three elasticities

related to the effect of agglomeration on the demand for each factor. The sum of the factor

elasticities equals the returns to scale as shown in the upper panel. The second column of the

bottom panel shows the estimated response of factor prices to higher effective density. The

patterns confirm the insights from the upper panel. Agglomeration is associated with more

efficient labour and capital inputs, and hence higher prices for those factors. The extent to

which labour demand is reduced depends on the own-price demand elasticity, which is shown

in the third column. Demand is relatively elastic for all three factors, with elasticities ranging

from -1.32 to -1.16 in the pooled specification and from –1.27 to –1.20 for the ‘within

enterprise’ specification. The final column shows the factor demand elasticities. The demand


36

for capital and labour are 9% to 15% lower in high-density areas (‘within enterprise’

specification), and the demand for intermediate consumption is raised by 12%.

The measures shown in table 5.4 can be calculated for each industry, based on industry-

specific regressions. Industry-specific patterns are summarised in table 5.5 (returns to scale

and agglomeration elasticity decomposition) and table 5.6 (factor elasticities). Elasticities are

calculated at industry-specific means. The caveats expressed above regarding the robustness

of the ‘within enterprise’ estimates of agglomeration elasticities apply a fortiori to the less

restrictive factor-augmenting specification. However, as is evident in Appendix table 2, and as

was seen in Appendix table 1 for the Hicks-neutral specifications, the precision of the

production function parameter estimates other than that of the agglomeration elasticity itself

is similar in the pooled and ‘within enterprise’ specifications, giving more confidence that

these ‘within enterprise’ estimates are not greatly affected by attenuation bias.

Table 5.5: Derived relationships: Scale and agglomeration from ‘within enterprise’ specification (by

one-digit industry)

Returns

to scale

Agglomeration

elasticity =

Labour

augmenting

+ Capital

augmenting

+ IntCons

augmenting

+ Direct

effect

(∂Y/∂U) (γlu*L) (γ

ku*K) (γ

iu*I) (α

u+γ

uu*U)

A

Agriculture, forestry

and fishing 1.023 -0.107 0.008 -0.180 0.042 0.022

B

Mining and

quarrying 0.997 0.022 -0.180 -1.195 0.409 0.988

C Manufacturing 1.069 -0.012 0.042 0.193 -0.462 0.215

E Construction 1.067 0.038 0.012 0.124 -0.377 0.280

F Wholesale trade 1.029 0.066 0.033 -0.020 -0.385 0.438

G Retail trade 1.071 0.037 0.046 0.140 -0.199 0.051

H

Accommodation,

cafes 1.073 -0.015 0.066 0.171 -0.493 0.241

I

Transport and

storage 1.081 0.032 0.017 0.119 -0.348 0.245

J

Communication

services 1.070 -0.026 0.023 0.176 -0.307 0.082

K

Finance and

insurance 0.898 -0.028 -0.014 0.278 -0.417 0.126

L

Property and bus

services 0.980 0.054 0.025 0.162 -0.361 0.228

N Education 1.123 0.065 0.082 -0.223 -0.642 0.848

O

Health and

community services 1.050 0.022 0.005 -0.087 0.010 0.094

P

Cultural and

recreation services 1.095 -0.014 0.004 0.134 -0.259 0.108

All industries 1.039 0.012 0.034 0.159 -0.532 0.351

5 Results

37

The variation in agglomeration elasticities across industries is relatively small; ranging from –

0.107 in agriculture, to 0.066 for wholesale trade. There is much greater variation, however,

in the contributions of different components. For instance, the direct effect of agglomeration

ranges from 0.022 for agriculture, to 0.848 for education, and the contribution of

intermediate consumption augmentation ranges from –0.642 in education to 0.042 in

agriculture (discounting estimates from the small mining industry). Some of this variation in

component contributions may be a consequence of imprecise estimation19 but for most

industries, the decomposition provides interpretable patterns. We discount the

decompositions for the relatively small mining and education industries.

The three industries with the highest estimated agglomeration elasticities in table 5.5

(wholesale trade, education, and property and business services) also had relatively large

agglomeration elasticities in table 5.2. In all three cases, there is a relatively large positive

direct effect of agglomeration, offset by a negative contribution from intermediate

consumption input being less efficient in more dense areas. With the exceptions of finance

and insurance and mining,20 labour efficiency is raised in all industries, although the effect

contributes relatively little compared with the direct effects and intermediates augmentation,

ranging from 0.004 to 0.082. In nine out of the 14 industries, the capital efficiency is higher

in denser areas, with a minimum contribution of 0.119.

Table 5.6 shows the implications of the patterns of factor augmentation on factor demands,

and also the factor output elasticities for each industry. Output elasticities range from 0.220

(agriculture) to 0.461 (education) for labour, from 0.099 (construction) to 0.283 (retail trade)

for capital, and from 0.420 (retail trade) to 0.635 (manufacturing) for intermediate

consumption. The fourth column of table 5.6 shows that most industries follow the general

pattern of agglomeration raising the demand for intermediates and reducing demand for

labour and capital inputs, with the reduction in labour demand being more pronounced.

Other than mining, all industries have own-price elasticities of demand for capital, labour,

and intermediates between -1.4 and -1.1, implying elastic factor demand. The patterns of

factor augmentation that give rise to the factor price responses to agglomeration, as shown

in the second column, thus translate fairly directly to factor demands.

19 For instance, the relatively small education industry (around 6000 observations on 1800 enterprises)

and mining industry (1300 observations on 310 enterprises) have the largest positive contributions from

a direct agglomeration effect (0.848 and 0.988 respectively) but also large negative contributions from

capital augmentation (-0.223 and -1.195).

20 The ‘within enterprise’ estimates for each of these industries are imprecise due to relatively small

numbers of enterprises and because geographic concentration results in limited variation in effective

density.


38

Table 5.6: Derived relationships: Factor elasticities from ‘within enterprise’ specification (by one-

digit industry)

Demand elasticities Output

elasticities

∂Y/∂X ∂Px/∂U ∂X/∂P

x ∂X/∂U

Labour

A Agriculture, forestry and fishing 0.220 0.056 -1.377 -0.077

B Mining and quarrying 0.329 -0.184 -1.926 0.354

C Manufacturing 0.292 0.096 -1.273 -0.122

E Construction 0.244 0.079 -1.360 -0.107

F Wholesale trade 0.378 0.081 -1.270 -0.102

G Retail trade 0.368 0.080 -1.250 -0.100

H Accommodation, cafes and restaurants 0.287 0.145 -1.342 -0.195

I Transport and storage 0.275 0.069 -1.271 -0.088

J Communication services 0.285 0.140 -1.210 -0.169

K Finance and insurance 0.295 -0.019 -1.152 0.022

L Property and business services 0.338 0.100 -1.252 -0.125

N Education 0.461 0.164 -1.335 -0.219

O Health and community services 0.405 0.015 -1.232 -0.019

P Cultural and recreational services 0.323 0.022 -1.248 -0.028

All industries 0.317 0.121 -1.268 -0.153

Capital

A Agriculture, forestry and fishing 0.232 -0.072 -1.178 0.085

B Mining and quarrying 0.144 -0.545 -2.044 1.114

C Manufacturing 0.142 0.124 -1.169 -0.144

E Construction 0.099 0.142 -1.152 -0.164

F Wholesale trade 0.202 -0.001 -1.175 0.001

G Retail trade 0.283 0.018 -1.199 -0.022

H Accommodation, cafes and restaurants 0.215 0.055 -1.294 -0.072

I Transport and storage 0.165 0.073 -1.195 -0.087

J Communication services 0.174 0.076 -1.142 -0.086

K Finance and insurance 0.175 0.185 -1.169 -0.217

L Property and business services 0.218 0.057 -1.231 -0.070

N Education 0.207 -0.101 -1.144 0.115

O Health and community services 0.209 -0.040 -1.218 0.049

P Cultural and recreational services 0.180 0.082 -1.182 -0.097

All industries 0.191 0.078 -1.208 -0.094

5 Results

39

Demand elasticities Output

elasticities

∂Y/∂X ∂Px/∂U ∂X/∂P

x ∂X/∂U

Labour

Intermediates

A Agriculture, forestry and fishing 0.572 0.008 -1.170 -0.009

B Mining and quarrying 0.524 0.256 -1.423 -0.365

C Manufacturing 0.635 -0.072 -1.200 0.086

E Construction 0.724 -0.046 -1.134 0.052

F Wholesale trade 0.450 -0.069 -1.241 0.085

G Retail trade 0.420 -0.079 -1.222 0.097

H Accommodation, cafes and restaurants 0.571 -0.094 -1.305 0.123

I Transport and storage 0.641 -0.048 -1.139 0.055

J Communication services 0.611 -0.088 -1.123 0.099

K Finance and insurance 0.428 -0.061 -1.167 0.071

L Property and business services 0.424 -0.106 -1.212 0.129

N Education 0.455 -0.122 -1.224 0.149

O Health and community services 0.436 0.005 -1.189 -0.006

P Cultural and recreational services 0.593 -0.037 -1.133 0.042

All industries 0.531 -0.100 -1.201 0.120


40

6 Summary and discussion

The paper presents the first set of agglomeration elasticity estimates directly estimated from

New Zealand microdata. The pooled cross-sectional patterns of elasticities by industry are

fairly similar to the existing estimates based on United Kingdom data currently used in the

Economic evaluation manual (NZTA 2008).

We estimate an aggregate pooled cross-sectional agglomeration elasticity of 0.171. There is

considerable variation in the size of estimated industry-specific agglomeration elasticities.

The largest estimates are for the finance and insurance (0.076), education (0.076), property

and business services (0.074), wholesale trade (0.072), and retail trade (0.065) industries.

The smallest estimate is for the agriculture, forestry and fishing industry (0.013).

These cross-sectional estimates may overstate the true impact of agglomeration on

productivity, as a result of the sorting of high-productivity firms into high-density areas. If the

estimated agglomeration effects reflect sorting rather than a causal effect, increases in

density as may result from investments in transport infrastructure will not necessarily result

in net increases in production.

We would prefer to rely on estimates that exclude the impact of firm heterogeneity and sorting

and to this end we present panel estimates of agglomeration elasticities that control to some

extent for these influences. We present ‘within local industry’ estimates that control for sorting

across regions and industries, and ‘within enterprise’ estimates that also control for sorting

within locations. The ‘within local industry’ estimates are generally similar, though slightly

larger, than the cross-sectional estimates. In contrast, the ‘within enterprise’ estimates are

generally much smaller than the corresponding pooled cross-sectional estimates, consistent

with the presence of sorting. Unfortunately, as a result of various statistical features of the data,

discussed in the paper, the ‘within enterprise’ estimates may understate the true causal effect

of agglomeration on productivity. We thus rely on the ‘within local industry’ estimates as

providing the most reliable indication of agglomeration elasticities.

Overall, allowing for industry differences in technology (production functions), the ‘within

local industry’ specification yields an agglomeration elasticity of 0.069. This varies across

industries, from industry-specific estimates ranging from 0.032 (agriculture, forestry and

fishing) to 0.087 (finance and insurance). Other high-elasticity industries are wholesale trade

(0.086), retail trade (0.086) and health and community services (0.083). There is evidence of

decreasing returns to agglomeration within all industries.

Agglomeration elasticities also vary across regions, from a low of 0.048 in Canterbury to a

high of 0.177 in Northland.21. High density regions of Canterbury, Wellington (0.063) and

Auckland (0.056) have lower agglomeration elasticities than less dense regions, consistent

with decreasing returns to agglomeration. We are unable to obtain reliable estimates for

territorial authorities within Auckland, with the exception of Auckland City (0.061).

We find that agglomeration generally increases the productivity of labour and capital inputs,

though the contributions of agglomeration through these channels is smaller than the direct

(factor-neutral) effect.

21 The estimated elasticity for Gisborne is higher (0.222) but is not statistically significant.

7 Future directions

41

7 Future directions

The current paper represents a significant advance in our knowledge of the relationship

between agglomeration and productivity in New Zealand. The analyses do, however, highlight

a number of issues that could usefully be investigated in future research.

1 Analysis of localisation effects: The estimates in the current paper capture only the

effects of overall effective density. It is plausible that, for at least some industries, it is

the density of own-industry employment that is most relevant for their productivity. The

analysis could be extended by estimating the elasticity of productivity with respect to

own-industry as well as overall density, adding and extra regression term: βUln(effdens) +

βOln(owneffdens/effdens).

2 More flexible measurement of density: First, the assumption of a constant distance decay

of 1 could be relaxed, to estimate the geographic extent of agglomeration effects and

detect differences in this across industries. Second, the assumption of a quadratic effect

of effective density on productivity could be relaxed to detect more general patterns of

non-linearity.

3 Dynamics of agglomeration effects: More analysis of the temporal extent of

agglomeration effects could be undertaken. The current paper has focused on the

concurrent relationship between effective density and productivity. However, the benefits

of density may accrue over time, in which case fixed effects estimates will understate the

true impact.

4 Alternative treatment of heterogeneity: Our attempts to control for enterprise

heterogeneity using the ‘within enterprise’ specification were beset by problems of

attenuation bias and lack of precision. An alternative means of controlling for

heterogeneity and sorting within as well as between locations is offered by a control-

function approach (Olley and Pakes 1996, Levinsohn and Petrin 2003, Ackerberg et al

2006). Re-estimating production functions and agglomeration elasticities using these

methods may provide more reliable estimates.


42

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44

Appendix A: Comparability between different data sources: AES and IR10

Records for enterprises with postal AES records contain derived measures of gross output

and intermediate consumption. For enterprises with IR10 records but no AES records, these

quantities have to be derived from reported items.

Capital services charges: For both data sources, we impute a capital service charge for firms

that rent or lease some of their capital inputs, and count transfer this imputed amount from

intermediate consumption to capital services. Rental leasing and rates costs are reported

separately on the IR10 form but not in AES. We express IR10 rental, leasing and rates costs as

a ratio to a subset of expenses that are measured consistently across the two data sets. We

then impute AES rental and leasing as the predictions from a group logit of that ratio as a

function of depreciation costs, asset values separately for vehicles, plant and machinery,

furniture and fittings, and land and buildings, all measured as a proportion of commonly

identified expenses, and year effects.

Purchases of goods for resale: The AES measure of gross output deducts purchases of

goods for resale from gross sales. An examination of industry-by-industry differences in

reported sales for firms with both AES and IR10 records suggests that in some industries,

many firms report resale purchases as part of intermediate consumption. We calculate, for

each two-digit industry and year, the ratio of AES total resale purchases to the sum of

intermediate consumption and resale purchases. We then apply this ratio to IR10

intermediate consumption to obtain imputed resale purchases. We adjust IR10 gross output

and intermediate consumption by subtracting imputed resale purchases from both.

Interest paid: For general finance and insurance industries, AES treats interest paid as a

deduction from gross output. IR10 records are treated in the same way.

Road user charges: These should not be included in intermediate consumption but are not

separately reported on IR10 forms. A proportion of IR10 intermediate consumption is

removed, based on the proportion of AES intermediate consumption accounted for by

(separately reported) road user charges.

Appendix tables

45

Appendix tables

Appendix table 1: Hicks-neutral aggregate translog production function: linear and quadratic

agglomeration effects

Linear agglomeration effects Quadratic agglomeration effects

Pooled

Within local

industry

Within

enterprise Pooled

Within local

industry

Within

enterprise

ln(effdens) 0.171** 0.048** 0.015** 0.360** -0.088* -0.402**

[0.001] [0.003] [0.005] [0.029] [0.042] [0.071]

ln(effdens) squared -0.009** 0.007** 0.020**

[0.001] [0.002] [0.003]

ln(capital) -0.147** -0.227** 0.220** -0.149** -0.227** 0.220**

[0.011] [0.011] [0.014] [0.011] [0.011] [0.014]

ln(labour) 1.330** 1.313** 1.136** 1.332** 1.312** 1.136**

[0.021] [0.020] [0.026] [0.021] [0.020] [0.026]

ln(intermediates) 0.117** 0.166** 0.175** 0.116** 0.167** 0.175**

[0.012] [0.012] [0.015] [0.012] [0.012] [0.015]

ln(cap)^2 0.030** 0.041** 0.026** 0.030** 0.041** 0.026**

[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

ln(cap)*ln(lab) -0.009** -0.025** -0.005** -0.010** -0.025** -0.005**

[0.002] [0.002] [0.002] [0.002] [0.002] [0.002]

ln(cap)*ln(int) -0.028** -0.034** -0.050** -0.028** -0.034** -0.050**

[0.001] [0.001] [0.001] [0.001] [0.001] [0.001]

ln(lab)^2 0.059** 0.050** 0.065** 0.059** 0.050** 0.065**

[0.002] [0.001] [0.002] [0.002] [0.001] [0.002]

ln(lab)*ln(int) -0.093** -0.081** -0.082** -0.094** -0.081** -0.082**

[0.002] [0.002] [0.002] [0.002] [0.002] [0.002]

ln(int)^2 0.040** 0.041** 0.043** 0.040** 0.041** 0.043**

[0.000] [0.000] [0.001] [0.000] [0.000] [0.001]

Dummy for AES observation 0.068** 0.008 0.059** 0.068** 0.008 0.060**

[0.005] [0.005] [0.009] [0.005] [0.005] [0.009]

Year dummies Y Y Y Y Y

Local Industry dummies Y Y

Enterprise dummies Y Y

Observations 1041300 1041300 1041300 1041300 1041300 1041300

Number of enterprises 886700 886700 886700 886700 886700 886700

R-squared 0.80 0.82 0.95 0.8 0.82 0.95


46

Appendix table 2: Translog coefficient estimates –fully interacting density effects

Pooled Within enterprise

αK -0.345** 0.086**

[0.018] [0.022]

αL 0.891** 0.677**

[0.032] [0.034]

αI 0.997** 0.678**

[0.018] [0.022]

αU 0.769** -0.379**

[0.034] [0.089]

γUU/2 0.005** 0.037**

[0.001] [0.004]

γKK/2 0.030** 0.027**

[0.001] [0.001]

γKL -0.006** -0.004*

[0.002] [0.002]

γKI -0.036** -0.055**

[0.001] [0.001]

γKU 0.027** 0.016**

[0.001] [0.002]

γLL/2 0.054** 0.061**

[0.002] [0.002]

γLI -0.088** -0.077**

[0.002] [0.002]

γLU 0.035** 0.040**

[0.002] [0.003]

γII/2 0.045** 0.045**

[0.000] [0.001]

γIU -0.092** -0.050**

[0.001] [0.002]

AES observation 0.102** 0.060**

[0.005] [0.008]

Year dummies Yes Yes

Constant -1.155** 5.089**

[0.245] [0.494]

Observations 886700 886700

Number of enterprises 250800

R-squared 0.80 0.52

Notes: Robust standard errors clustered at the enterprise level. **: significant at 1%; *: significant at 5%.

R-squared for the fixed effect column is calculated for within-enterprise variation

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